Both Cessna and Piper make turboprops, there are also several aftermarket "upgrades" for aircraft like the C-210
and Beech Bonanza. As Eagl has mentioned, cost is the determining factor.
Piper Meridian aka Turboprop Malibu
http://www.piper.com/pages/Meridian.cfm
Cessna Caravan
http://www.cessna.com/caravan.html
Yup, I'm aware of that.. they are both $2 million+ planes, both Cessna and Piper also make turbofans too. That's apples and oranges to what I'm talking about.
I'm talking about smaller hp turboprops for light singles and twins like a 172, 182, SR-22, Archer, Baron, DA-40, Acclaim, 206 etc...
I've seen Bonanzas and Barons with PT-6s (and that Lancair kit). With is really stupid I think, they take a PT-6 which can be rated at over 1000hp and derate it to 400hp, when a much smaller lighter turbine like an Allison 250 can make that kind of power. There are STCs out there for putting a 250 on certain airframes. Like the Tradewinds Bonanza, they charge like $400k or something for the conversion, but they're in the business of making money off their STC, I'm sure a production plane with a similar turbine from the factory would not add nearly as much to the price.
The cost for small hybrid turbines is coming down a lot, and as we get better at metallurgy and manufacturing they will come down more. Rolls Royce hinted that they can sell the new RR500 (updated Alison 250) for less then $100k (to Mooney at least), with comparable hp to any TCM or Lycoming TSIO 5xx. I had to look up a new TCM TSIO 540 the other day, $65K rebuilt, $80K new.
So think about it, when some one is going to drop $600K to $800K on something like a new Cirrus SR-22, or Cessna Corvalis, or Mooney Acclaim, do you think they are going to balk at another $40-50K (or even $50-100K after the airframe mfctr mark up) on the price, when for that they get all the benefits of a turbine (faster, lighter, more reliable, cheaper fuel, more available fuel, no lead fouling, longer TBO, smoother operation, etc.) Plus manufacturers could use the same turbine for many different airframes, meaning more bulk production and cheaper engines. For example I know an Allison 250 can be rated anywhere between 200 and 500 shaft horsepower, just by changing the fuel metering (all the engine internals, except for maybe fuel nozzles are the same). So if we take Cessna, they could have a 200hp version for the 172, a 250hp version for the 182, and a 350hp version for the Corvalis and 206 etc.. Without having to buy 3 different engines. And because turbines are most efficient at 100% you'll be faster for the same hp as well, which negates the greater GPH fuel burn of turbines. This would make turbines more popular and more affordable, and then I could see a whole bunch of STCs popping up for turbine retrofits on older planes.
The reliability of turbines blows recips away. In the oil and gas industry they use natural gas powered turbines to pump oil and gas. They run them at 100% power 24/7 for months on end, they add oil while it's running and only shut them down for scheduled maintenance and inspections. Same story with those who use turbines for electricity production. With small turbines for small planes the most common damage would be bearing or turbine blade/nozzle damage from overtemp and hot starts. Just keep the oil temp/pressure and EGT and TIT in the green and they will run forever, and with a modern ECU to control start/stop and fuel metering like on APU's it would be near impossible to have a hot start, overtemp or overspeed it. Also there is the possibility of FOD damage or blade rubs, but the compressor inlet is so small on these that FOD damage is unlikely and you'd probably hear a blade rub before it became catastrophic.
Another turbine advantage would be pressurized light twins, like a Beech Baron, or Cessna 340. The way they do it now is stupid IMO. They put a turbo on so they can fly higher, then they rob engine of half the air coming from the turbo to pressurize the cabin. With even a small turbine there is plenty of bleed air not doing anything else to pressurize the cabin, without the turbine even breaking a sweat running at 100%.
I love classic planes, warbirds, radial engines and such (in fact I'm excited because I get to work on some next week). I just think it's crazy that brand new GA planes rolling off the assembly line today are using the same powerplant technology as they where 60 years ago. Look at all the advances in avioncs and navigation, with stuff like glass panels, synthetic vision, moving maps, GPS, TCAS, XM weather. And yet driving the plane is the same inefficient pistons, con rods, push rods, lifters, rockers, springs, valves, camshafts, magnetos, carburetors, fuel injectors, turbochargers etc, that we've been using since the 1940's.